Method of manufacturing a semiconductor device

ABSTRACT

A method of manufacturing a semiconductor device is provided. The method includes transferring an internal shot and an external shot by performing a patterning process on a first wafer, analyzing an overlay of the first wafer, and performing a lithography process on a second wafer, based on the analyzing of the overlay of the first wafer, wherein the analyzing of the overlay of the first wafer includes providing, to the first region, first augmented overlays generated based on an orthogonal coordinate system using first and second directions perpendicular to each other as an axis, and providing, to the second region, second augmented overlays that are overlays in a radial direction from the center of the first wafer.

CROSS-REFERENCE TO RELATED APPLICATION

This application is based on and claims priority under 35 U.S.C. § 119to Korean Patent Application No. 10-2021-0000988, filed on Jan. 5, 2021,in the Korean Intellectual Property Office, the disclosure of which isincorporated by reference herein in its entirety.

BACKGROUND

The inventive concept relates to a method of manufacturing asemiconductor device. More particularly, the inventive concept relatesto a method of manufacturing a semiconductor device having an improvedreliability and an improved manufacturing yield.

With a reduction in a memory cell size for recent high integration ofinformation communication devices, operations of memory devices andstructures of operational circuits and/or interconnection lines includedin the memory devices become more complicated. Accordingly, applicationof an extreme ultraviolet (EUV) lithography is increasing in themanufacture of semiconductor devices. The EUV lithography uses lighthaving a wavelength in a range of, for example, 4 nm to 124 nm, morepreferably, a wavelength of 13.5 nm, and enables superfine dimensionprocessing of 20 nm or less (sub-20 nm) that is difficult to implementaccording to an existing lithography technique using ArF excimer laserlight.

A feedback process through highly-reliable and highly-precise overlaymeasurement and analysis is one of the core elements for securing thereliability of the EUV lithography. Thus, various research intoimproving the precision and reliability of overlay measurement is beingcarried out.

SUMMARY

The inventive concept provides a method of manufacturing a semiconductordevice having an improved reliability and an improved manufacturingyield.

Additional aspects will be set forth in part in the description whichfollows and, in part, will be apparent from the description, or may belearned by practice of the presented embodiments.

According to an aspect of the inventive concept, there is provided amethod of manufacturing a semiconductor device. The method includestransferring an internal shot and an external shot by performing alithography process and a patterning process based on the lithographyprocess on a first wafer, wherein the internal shot is within a criticalradius from a center of the first wafer, and the external shot includesa first region within the critical radius from the center of the firstwafer and a second region outside the critical radius; measuring anoverlay of the first wafer patterned by the patterning process;analyzing the overlay of the first wafer; and performing a lithographyprocess on a second wafer, based on the analyzing of the overlay of thefirst wafer. The analyzing of the overlay of the first wafer includesproviding, to the first region, first augmented overlays generated basedon an orthogonal coordinate system using first and second directionsperpendicular to each other as an axis; and providing, to the secondregion, second augmented overlays that are overlays in a radialdirection from the center of the first wafer.

According to another aspect of the inventive concept, there is provideda method of manufacturing a semiconductor device. The method includestransferring a circuit pattern on an extreme ultraviolet (EUV) photomaskto a photoresist layer formed on a wafer, wherein a plurality of shotsthat are portions of the wafer to which the circuit pattern on the EUVphotomask has been transferred include a first region within a criticalradius from a center of the wafer and a second region outside thecritical radius; forming a photoresist pattern having a shapecorresponding to the EUV photomask, by developing the photoresist; andinspecting the photoresist pattern. The inspecting of the photoresistpattern includes measuring overlays indicating misalignment between apattern formed below a photoresist of the second region and thephotoresist pattern; processing the overlays of the second region suchthat the overlays of the second region are parallel to a radialdirection; and providing, to a plurality of locations on the secondregion, first augmented overlays in the radial direction from the centerof the wafer, based on the processed overlays.

According to another aspect of the inventive concept, there is provideda method of manufacturing a semiconductor device. The method includestransferring a circuit pattern on a photomask to a wafer, wherein eachof a plurality of shots that are portions of the wafer to which thecircuit pattern on the photomask has been transferred includes a firstregion within a critical radius from a center of the wafer and a secondregion outside the critical radius; measuring overlays representing aninterlayered misalignment of the plurality of shots; providing firstaugmented overlays to the first region of a first shot from among theplurality of shots, based on overlays included in the first region ofthe first shot; providing second augmented overlays to the second regionof the first shot, based on overlays included in the plurality of shots;and calculating an overlay model representing an overlay of an arbitrarylocation on the entire surface of the first shot by regression-analysison the first and second augmented overlays.

According to another aspect of the inventive concept, there is provideda method of manufacturing a semiconductor device, the method includingtransferring a circuit pattern on a photomask to each of a plurality offirst wafers included in a first lot, wherein each of a plurality ofshots to which the circuit pattern on the photomask has been transferredincludes a first region within a critical radius from a center of thewafer and a second region outside the critical radius; obtaining anoverlay of the plurality of first wafers to which the circuit pattern onthe photomask has been transferred; analyzing the overlay of the firstwafers; and performing a lithography process on second wafers includedin a second lot, based on the analyzing of the overlay of the firstwafers of the first lot. The analyzing of the overlay of the firstwafers of the first lot includes providing first augmented overlays tothe first region of a first shot from among the plurality of shots,based on overlays included in the first region of the first shot;processing the overlays of the second region such that the overlays ofthe second region extend in a radial direction; providing secondaugmented overlays to the second region of the first shot, based on theprocessed overlays of the second region; and performing regressionanalysis on the first and second augmented overlays.

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary embodiments of the inventive concept will be more clearlyunderstood from the following detailed description taken in conjunctionwith the accompanying drawings in which:

FIG. 1 is a flowchart of a method of manufacturing a semiconductordevice, according to example embodiments;

FIG. 2 is a plan view of a full shot and a partial shot within a wafer;

FIGS. 3A and 3B are magnified partial plan views of a full shot and apartial shot of FIG. 2 ;

FIGS. 4 and 5 are flowcharts for explaining a wafer inspection includedin a method of manufacturing a semiconductor memory device, according toexample embodiments;

FIGS. 6 through 9 are plan views for explaining an inspection, accordingto example embodiments; and

FIGS. 10 and 11 are flowcharts for explaining a method of manufacturinga semiconductor memory device, according to example embodiments.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Embodiments will now be described more fully with reference to theaccompanying drawings. In the accompanying drawings, like referencenumerals may refer to like elements, and repeated descriptions of thelike elements will be omitted.

FIG. 1 is a flowchart of a method of manufacturing a semiconductordevice, according to example embodiments.

FIG. 2 is a plan view for explaining a method of manufacturing asemiconductor device, according to example embodiments. FIG. 3A is amagnified partial plan view of one of full shots FS of FIG. 2 , and FIG.3B is a magnified partial plan view of one of partial shots PS of FIG. 2. The full shot FS of FIG. 3A and the partial shot PS of FIG. 3B areeach outlined in bold in FIG. 2 .

Referring to FIGS. 1 and 2 , in P10, a lithography may be performed onwafers W of a first lot.

The lithography may include processes such as adhesion promotion, spincoating, soft bake, exposure, post-exposure bake, development,after-development inspection, and hard bake.

A photoresist material may lack adhesion to the surface of silicon or asilicon-containing material. In the adhesion promotion, photoresist isattached to a wafer W or circuit patterns formed on the wafer W.Accordingly, before the photoresist material is provided onto the waferW, the adhesion promotion may be performed on the surface of the waferW. A representative example of the adhesion promotion is processing thesurface of the wafer W with hexamethyldisilazane (HMDS). Because HMDS isable to make the surface of the wafers W hydrophobic, HMDS may improveadhesion between the photoresist material and the wafer W.

Then, the spin coating may be performed. In the spin coating, aphotoresist material layer is provided on the wafer W. The photoresistmaterial may be formed from organic polymer provided in asolution-state. To coat the wafer W with the photoresist material, thewafer W provided with a solution-state photoresist may be spin-rotatedat a high speed. As an excess resist is taken out by the spin rotationof the wafer W and a solvent evaporates, a thin solid photoresist layermay be provided.

A material used to form the photoresist layer may be sensitive toultraviolet (UV) light, deep UV (DUV) light, extreme UV (EUV) light,excimer laser beams, X rays, or electrons. In an EUV exposure process,the number of photons during exposure is less than that in an exposureprocess such as DUV, and thus, a material having a high EUV absorptionrate is used. Thus, a photoresist material for EUV may include, forexample, hydroxy styrene, which is a polymer. Iodophenol may be providedas additives to EUV photoresist.

According to some embodiments, a thickness of the photoresist layer mayrange from about 0.1 μm to about 2 μm. According to some embodiments,the thickness of the photoresist layer may range from about 200 nm toabout 600 nm. The EUV photoresist may be provided with a small thicknessby spin-coating a dilute photoresist solution.

In some cases, the EUV photoresist may include an inorganic materialsuch as tin oxide. In this case, even when the EUV photoresist isremoved through a strip process after the lithography process andsubsequent processes are finished, the inorganic material may remain inan underlying layer of the photoresist at a concentration of about1*10¹¹/cm³. When an inorganic material is used as photoresist, it iseasy to reduce the thickness of the photoresist, and etch selectivity ishigh, and thus, a hard mask disposed under the photoresist may beimplemented to be thin.

When a layer to be etched has a large thickness, a hard mask layerincluding amorphous carbon may be further provided under thephotoresist. According to some embodiments, the hard mask layer mayfurther include fluorine. When the hard mask layer includes fluorine,EUV sensitivity of the photoresist may be improved. An anti-reflectionlayer may be further provided between the hard mask layer and thephotoresist.

According to some embodiments, a soft bake process may be selectivelyperformed after the spin coating process. In some cases, the density ofthe photoresist material layer coated on the wafer W may be insufficientto conduct a subsequent process. The soft bake process may densify thephotoresist material layer and remove solvent that remains on thephotoresist material layer. The soft bake process may be performed by abake plate included in a lithographic apparatus. The wafer W, on whichthe soft bake process has been performed, may be selectively cooled by achill plate.

Thereafter, referring to FIGS. 1 through 3B, an exposure process may beperformed. In the exposure process, a pattern previously formed on apatterning device such as a lithographic mask is transferred to thewafer W. In the exposure process, a radiation beam having across-section set by the patterning device may be radiated onto thewafer W.

The radiation beam may include UV rays, DUV rays, EUV rays, an excimerlaser beam, X rays, electron rays, and the like. According toembodiments, a wavelength of EUV rays may range from about 4 nm to about124 nm. According to embodiments, the wavelength of EUV rays may rangefrom about 5 nm to about 20 nm. According to embodiments, the wavelengthof EUV rays may range from about 13 nm to about 14 nm. According toembodiments, the wavelength of EUV rays may be about 13.5 nm.

A radiation system for generating EUV rays may include a laser to excitea plasma source to provide plasma, and a source collector module tostore the plasma. For example, plasma may be generated by radiating alaser beam to a plasma source such as tin particles and Xe gas or Livapor. Such a radiation system is generally referred to as alaser-produced plasma (LPP) source. Alternative sources include adischarge plasma source or a source based on synchrotron radiationprovided by an electron storage ring.

According to some embodiments, the patterning device may be oftransmissive or reflective type. The patterning device may be one of,for example, a mask, a programmable mirror array, and programmable LCDpanels. When the patterning device is of a mask type, the patterningdevice may be a binary type, an alternating phase-shift type, and anattenuated phase-shift type, or any one of various hybrid types, butembodiments are not limited thereto.

When the patterning device is a programmable mirror array, thepatterning device may include, for example, a set of small mirrorsarranged in a matrix form. The small mirrors included in the patterningdevice may be individually tilted to reflect radiation beams incident onthe small mirrors in different directions, respectively. The tiltedsmall mirrors may form patterns in radiation beams reflected by themirror matrix, respectively.

An EUV photomask, which is an example of the patterning device, mayinclude a silicon substrate, and a plurality of silicon layers andmolybdenum layers alternately arranged on the silicon substrate. Aruthenium (Ru)-containing layer may be further provided on the pluralityof silicon layers and molybdenum layers alternately stacked. A layoutpattern composed of a tantalum boron nitride (TaBN)-containing layer anda Lawrencium-containing layer may be formed on the Ru-containing layer.The various materials and layers disclosed herein for the EUV photomaskare for illustrative purposes only and do not limit the technical spiritof the inventive concept in any sense.

In the exposure process, the properties of a photoresist material layerare partially changed to provide a photoresist pattern for forming asemiconductor circuit. Photoresist is a material that causes aphotochemical reaction to light exposure. The photoresist material layermay be partially exposed by a patterning device such as a photomask. Byprojecting light transmitted by the patterning device onto thephotoresist material layer, a circuit pattern of one layer thatconstitutes a semiconductor device may be transferred to the photoresistmaterial layer on the wafer W.

The exposure process may be performed based on measurement of analignment mark AGNM formed on the wafer W. By identifying the locationof the alignment mark AGNM before exposure, a difference between thelocation of an alignment mark AGNM designed to form an underlying layerand the location of an alignment mark AGNM actually implemented in theunderlying layer may be determined. By identifying the location of thealignment mark AGNM from a plurality of locations on the wafer W andthen performing regression analysis on the identified location, a modelfunction representing a difference between a designed location and anactual location may be determined for an arbitrary element on the waferW.

According to embodiments, locations of alignment marks AGNM may beidentified by a plurality of light beams having different wavelengths.For example, when the locations of the alignment marks AGNM areidentified by light beams of four different wavelengths, four modelfunctions corresponding to the light beams of four different wavelengthsmay be provided, and the exposure process may be performed based on acombined model function generated based on a weighted sum of the fourmodel functions.

Because a semiconductor device is manufactured by using a series ofpatterning processes with respect to a plurality of vertically stackedmaterial layers, alignment of a new layer with respect to apreviously-formed circuit pattern is a key factor in increasing theyield of semiconductor device manufacturing.

An EUV exposure process may be performed by axial projection (e.g.,about 4:1 axial projection). Because a mask pattern is reduced to a sizeof about ¼ and transferred to the wafer W, a full shot may eventuallycorrespond to a size of about ¼ of the entire mask pattern. Here, ¼ is areduction ratio of the length, and may correspond to a reduction ofabout 1/16 in terms of area. Accordingly, a pattern formed on the EUVphotomask has a larger critical dimension than a pattern actuallytransferred to the wafer W, and thus, the accuracy of the pattern may beimproved, and accordingly, the reliability of a lithography processusing the EUV photomask may be improved.

Here, exposure methods may be classified into a scanning method forcontinuously photographing and a step method for photographing step bystep. Because the EUV exposure process is generally performed by ascanning method, an EUV exposure apparatus is generally referred to as ascanner. Further, the EUV exposure apparatus may perform scanning byusing a slit that restricts light to a partial area of a mask. The slitmay be an optical element that restricts light in an apparatus forperforming an EUV exposure process so that the light is uniformlyradiated to an EUV mask. The light is limited to be radiated to apartial area of the mask through the slit, but the light may becontinuously radiated while moving the mask in a direction opposite to ascanning direction. A region on the test wafer W, onto which light isradiated through scanning over the entire area of the mask as describedabove, may be a full shot FS.

According to some embodiments, a space on the wafer W may be filled witha liquid having a high refractive index, such as water. Accordingly, atleast a portion of the wafer W may be covered with the liquid. Theliquid is referred to as an immersion liquid, and the wafer W beingimmersed may refer to not only the wafer W being immersed in the liquidbut also the immersion liquid being placed on the path of a radiationbeam for performing exposure.

Two directions parallel to an upper surface of the wafer W andsubstantially perpendicular to each other are referred to as an Xdirection and a Y direction. A direction substantially perpendicular tothe upper surface of the wafer W is referred to as a Z direction. The Xdirection and the Y direction may be directions distinguished from eachother. In more detail, the Y direction may be a direction in whichscanning is performed during scanning-type exposure. The X direction maybe a direction substantially perpendicular to the direction in which thescanning proceeds, and this description is equally applied to all thedrawings below.

The full shot FS is a region on the wafer W to which the entirety of apattern formed on a patterning device such as a lithography mask istransferred. A plurality of chip regions CHP may be defined within onefull shot FS. The plurality of chip regions CHP may be regions in whicha plurality of circuit layouts for forming a semiconductor device areoverlapped with each other and accordingly, a semiconductor chip isformed. According to some embodiments, the full shot FS may have, but isnot limited to, a size of about 26 mm on the x axis and about 33 mm onthey axis. One full shot FS may include various numbers and sizes ofchip regions CHP according to the type and specification of a device tobe formed.

The partial shot PS is a region on the wafer W to which a portion of thepattern formed on the patterning device such as a lithography mask istransferred, because shots located in an outer portion of the wafer W donot form full shots due to the circular shape of the wafer W.Accordingly, when an exposure process is performed on the outer portionof the wafer W, only a portion of the mask pattern may be transferred tothe wafer W.

Each of the full shots FS and the partial shots PS may include chipregions CHP and scribe lines SL of the chip regions CHP. The scribelines SL may extend between the chip regions CHP and may separate thechip regions CHP from one another horizontally (i.e., any one of the Xdirection and the Y direction). The scribe lines SL may be a region forseparating a semiconductor chip formed on the chip regions CHP intoindividual devices via a sawing process.

Although FIGS. 3A and 3B illustrate that each of the chip regions CHPhas an approximately square profile, embodiments of the inventiveconcept are not limited thereto. For example, chips may be driverdriving IC chips. In this case, a pair of opposite sides of the chipsmay be longer than another pair of opposite sides of the chipsperpendicular to the former pair of opposite sides. For example, thechips may have a rectangular profile.

According to some embodiments, a memory device may be formed within thechip regions CHP. According to some embodiments, a non-volatile memorydevice may be formed within the chip regions CHP. According to someembodiments, the non-volatile memory device may be a non-volatileNAND-type flash memory. According to some embodiments, the non-volatilememory device may be PRAM, MRAM, ReRAM, FRAM, or NOR flash memory. Avolatile memory device in which data is lost when power is cut off, suchas DRAM or SRAM, may be formed within the chip regions CHP. According tosome embodiments, for example, a logic chip or any one of a measuringdevice, a communication device, a digital signal processor (DSP), or asystem-on-chip (SoC) may be formed within the chip regions CHP.

An alignment mark AGNM and overlay marks OVM may be further formed onthe scribe lines SL of the full shots FS and the partial shots PS.According to some embodiments, the alignment mark AGNM and the overlaymarks OVM are formed on only the scribe lines SL. However, embodimentsof the inventive concept are not limited thereto. For example, some ofthe alignment mark AGNM and the overlay marks OVM may be formed withinthe chip regions CHP.

According to some embodiments, the alignment mark AGNM may be a patternused to accurately set an exposure region of lithography. According tosome embodiments, the alignment mark AGNM may be arranged adjacent to acenter portion of the full shot FS. However, embodiments of theinventive concept are not limited thereto. Each of a full shot FS and apartial shot PS is illustrated as including one alignment mark AGNM, butembodiments are not limited thereto. For example, some of the full shotsFS and the partial shots PS may include two or more alignment marksAGNM. Some of the full shots FS and the partial shots PS may include noalignment marks AGNM.

According to some embodiments, the overlay marks OVM may be patterns formeasuring an overlay. According to some embodiments, the overlay marksOVM may be arranged with a higher density than the alignment mark AGNM.Marks having various functions may be further formed on the scribe linesSL of the full shots FS and the partial shots PS. For example, a markfor electrically testing the characteristics of a completedsemiconductor device, a mark for measuring the thickness of an uppermostlayer after chemical mechanical polishing (CMP) is performed, and a markfor optically measuring a critical linewidth or an internal thicknessmay be further provided to the full shot FS.

The overlay marks OVM and the alignment mark AGNM may have a box in boxstructure or a grating structure. The overlay marks OVM and thealignment mark AGNM in a box in box structure may need an exclusiveregion where other overlay marks OVM and other alignment marks AGNM arenot formed so that proper overlay measurement is performed. Overlaymarks OVM having a grating shape need no exclusive regions, and may beprovided with a higher density than overlay marks OVM having a box inbox shape. Accordingly, the overlay marks OVM having a grating shape mayprovide more information than the overlay marks OVM of a box in boxshape, through overlay measurement.

After the exposure process, a bake process may be selectively performedbefore a development process. The bake process after exposure may beperformed by a bake plate. The bake process after exposure is aselective baking process used to induce uniformity improvement of aphotoresist layer through an additional chemical reaction or diffusionof a specific component within the photoresist layer.

Then, via the development process, a photoresist pattern may be formedon the wafer W. The photoresist pattern may be formed by a developer. Anexposed portion of the photoresist material layer may change to besoluble (for positive photoresist) or to be insoluble (for negativephotoresist). In the developing process, an exposed and soluble portionof the photoresist material layer (in the case of a positivephotoresist) or a portion that has not been exposed and remains soluble(in the case of a negative photoresist) is removed.

Then, referring back to FIG. 1 , in P20, an etch process may beperformed on the wafers W of the first lot. The etching process may be adry or wet etch process. The dry etch process may be, for example,reactive ion etching (ME), deep ME (DRIE), ion beam etching (IBE), or Armilling. As another example, a dry etch process capable of beingperformed on the wafer W may be atomic layer etching (ALE). A wet etchprocess capable of being performed on the wafer W may be an etch processthat uses at least one of Cl₂, HCl, CHF₃, CH₂F₂, CH₃F, H₂, BCL₃, SiCl₄,Br₂, HBr, NF₃, CF₄, C₂F₆, C₄F₈, SF₆, O₂, SO₂, and COS as an etchant gas.

Then, in P30, the wafers W of the first lot may be inspected. Theinspection of the wafer W may include inspection of patterncharacteristics including: i) accuracy of the size, shape and profile offeatures included in a pattern newly formed by the etching process; ii)measurement and calculation of an overlay indicating consistency (ormisalignment) between a preceding layer and the pattern newly formed bythe etching process; and/or iii) presence or absence of defects in thepattern formed by the etching process. According to embodiments, thewafer W may be inspected by a scattering optical system. However,embodiments are not limited thereto, and the wafer W may be inspected byan image based optical system.

According to embodiments, structural characteristics of the overlaymarks OVM may be calculated by measuring light diffracted by the overlaymarks OVM. The structural characteristics of the overlay marks OVM maybe calculated through wave analysis, nonlinear regression, and/orcomparison with a library of simulated spectra. Because a general shape(i.e., a designed shape) of the profiles of the overlay marks OVM isknown and some parameters for a structural change may be derived fromthe manufacturing process, the structural properties of the overlaymarks OVM may be calculated using parameters derived from scatteringspectral data. The structural properties of the overlay marks OVM mayinclude an overlay indicating accuracy (or misalignment) between thepreceding layer and the pattern newly formed by the etching process.

According to embodiments, the overlay may be further measured from thepattern within the chip regions CHP. In more detail, patterns forconstituting the semiconductor devices formed within the chip regionsCHP may be formed by the etch process of P20. An overlay value withinthe chip regions CHP may be obtained by measuring misalignment betweenthe pattern newly formed within the chip regions CHP in P20 and apattern overlapped with the newly formed pattern.

The inspection of the wafer W in P30 will now be described in moredetail with reference to FIG. 4 .

FIG. 4 is a flowchart of obtainment of an overlay model, according tosome embodiments.

Referring to FIGS. 2 through 4 , the inspection (P30) of the wafer W mayinclude measuring an overlay (P31), performing a first overlayregression analysis with respect to internal shots (P33), and performinga second overlay regression analysis with respect to external shots(P35).

Based on a critical circle CC defined by a critical radius RC within thewafer W, a first region R1 having low radial dependency and a secondregion R2 having high radial dependency may be defined. In more detail,a portion of the wafer W within the critical circle CC is defined as thefirst region R1, and a portion of the wafer W outside the criticalcircle CC is defined as the second region R2. The critical radius RC mayextend from a wafer center WC to the circumference of the criticalcircle CC.

The radial dependency of a specific portion of the overlay being largerefers to that the size of the specific portion of the overlay mainlydepends on a linear distance from the wafer center WC of the wafer W andthe direction of the overlay is substantially parallel to a radialdirection.

Some of the full shots FS may be arranged within the first region R1.Each of the full shots FS within the first region R1 is referred to asan internal shot. The partial shots PS and some of the full shots FSextend over the first region R1 and the second region R2. Accordingly,the partial shots PS and some of the full shots FS may include the firstregion R1 and the second region R2. The full shots FS and the partialshots PS including the first region R1 and the second region R2 will nowbe referred to as external shots. The external shots are displayed asdot patterns in FIGS. 3A and 3B so as to be distinguished from theinternal shots.

In FIGS. 3A and 3B, the wafer W has a radius of 150 mm and a criticalradius RC of 138.5 mm, 56 internal shots are included, and 50 externalshots are included. However, this is merely an example and the technicalspirit of the inventive concept is not limited thereto. The criticalradius RC may be set differently according to the size of the wafer Wand process characteristics, and thus, the numbers of internal shots andexternal shots may also vary.

Referring to FIGS. 2 through 4 , in P33, the first overlay regressionanalysis may be performed on the internal shots. The overlay marks OVMmay be arranged at a finite number of discrete locations on the wafer Was shown in FIGS. 3A and 3B. According to some embodiments, consecutiveoverlay values for the entire surface of the wafer W may be obtained byapplying a well-known fitting technique to overlay information measuredfrom the overlay marks OVM. According to some embodiments, the firstoverlay regression analysis may include regression-analyzing overlays inthe X direction and the Y direction respectively measured from theoverlay marks OVM by using an orthogonal polynomial as a basis.

An overlay model dx in the X direction and an overlay model dy in the Ydirection of the internal shots calculated by the first overlayregression analysis may be expressed as in Equation 1.dx=k1+k3·x+k5·y+k7x ² +k9xy+k11y ²+dy=k2+k4·x+k6·y+k8x ² +k10y ² +k12y ²+  [Equation 1]

where x indicates a location coordinate on the wafer W in the Xdirection, and y indicates a location coordinate on the wafer W in the Ydirection. In Equation 1, k1 through k12 indicate correction parametersthat are determined by the first regression analysis. For example, k1and k2 indicate parameters for correcting a parallel movement error, k3and k6 indicate parameters for correcting a scaling error, and k4 and k5indicate parameters for correcting a rotation error.

In Equation 1, the overlay models have been described based on apolynomial. However, this is merely an example, and the technical spiritof the inventive concept is not limited thereto. The overlay models maybe based on a complete basis set of a function space including adiscontinuous Chebyshev polynomial, a Zernike polynomial, and a discreteorthogonal polynomial. The complete basis set refers to a set of basesincluding a minimum number of bases that may represent an arbitraryfunction on the function space.

In Equation 1, parameters of a polynomial less than or equal to a secondpower are specified. However, depending on the objective of overlaymodeling and correction through the overlay modeling, the overlay modelsmay include parameters of a third or higher order polynomial. Forexample, the overlay models may include parameters of a seventh orderpolynomial. During an overlay regression analysis, the terms of higherorder than a correction range are referred to as residuals. For example,when a range of calculation and correction of overlay parameters isperformed by a seventh order polynomial, terms of eighth order orgreater may be residuals of the overlay regression analysis.

According to some embodiments, parameters including the correctionparameters k1 through k12 may be determined by a least square method.According to some embodiments, the first overlay regression analysis mayinclude determining the parameters including the correction parametersk1 through k12 in order to minimize a deviation between the values ofoverlays measured by the overlay marks OVM and the values of the overlaymodels according to Equation 1. In more detail, the first overlayregression analysis may include determining the parameters including thecorrection parameters k1 through k12 in order to minimize each of theformulas included in Equation 2 below.

$\begin{matrix}{{\sum\limits_{i}\left( {{dx_{i}} - {d{x(i)}}} \right)^{2}}{\sum\limits_{i}\left( {{dy}_{i} - {d{y(i)}}} \right)^{2}}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

where dx_(i) and dy_(i) indicate overlay values of an i-th overlay markOVM on a wafer in the X direction and the Y direction, respectively. InEquation 2, i indicates an ordinal number for identifying differentoverlay marks on the wafer. In Equation 2, dx(i) and dy(i) are values ofoverlay models that are calculated for location coordinates of the i-thoverlay mark OVM, respectively.

Then, in P35, the second overlay regression analysis may be performed onthe external shots.

The execution of the second overlay regression analysis with respect tothe external shots will now be described in more detail with referenceto FIGS. 5 through 9 .

FIG. 5 is a flowchart of a second overlay regression analysis accordingto some embodiments.

FIGS. 6 through 9 are views for explaining the second overlay regressionanalysis according to some embodiments. In more detail, FIGS. 6, 7, and9 illustrate overlays measured from the overlay marks OVM and/orpatterns formed within the chip regions CHP of FIG. 3A, and FIG. 8illustrates a portion of the wafer W to illustrate overlay datatransformation of P37.

In FIGS. 6, 7, and 9 , illustration of the chip regions CHP, the overlaymarks OVM, and the alignment mark AGNM is omitted, and arrows indicatesizes and directions of the measured overlays.

Referring to FIG. 5 , the performing (P35) of the second overlayregression analysis with respect to the external shots may includeproviding a first augmented overlay to the first region R1 of themagnified partial plan view of the full shot FS illustrated in FIG. 3A(P36), processing a measured overlay of the second region R2 (P37),providing a second augmented overlay to the second region R2 (P38), andperforming an overlay regression analysis with respect to the externalshots, based on the first and second augmented overlays (P39).

Referring to FIGS. 5 through 7 , in P36, the first augmented overlay maybe provided to the first region R1. For example, the first augmentedoverlay may be provided to the first region R1 based on an orthogonalcoordinate system using the X direction and the Y direction as an axis.In FIG. 7 , the locations of augmented overlays are indicated by squarepoints. Hereinafter, measurement-based overlays are referred to asmeasured overlays to be distinguished from augmented overlays in P36 andP38.

The first augmented overlays may be generated according to an arbitrarywell-known fitting method based on the measured overlays on the firstregion R1. The overlays augmented to the first region R1 may begenerated through a similar method to the overlay regression analysisdescribing only the measured overlays included in the first region R1 ofeach of the full shots FS through Equations 1 and 2. According toembodiments, the first augmented overlays may be aligned in the Xdirection and the Y direction so as to constitute at least some of therows and columns of a certain grid GR. According to embodiments, atleast some of the first augmented overlays may extend in a directionintersecting with the radial direction.

Then, referring to FIGS. 5 and 8 , in P37, the measured overlay of thesecond region R2 may be processed. For example, the overlays of thesecond region R2 may be processed such that the overlays are parallel tothe radial direction.

The processing of the measured overlay may include extracting a radialoverlay OVR from each overlay OV. A component perpendicular to theradial direction for each overlay OV may be processed as an overlayerror ΔOV.

Processing of overlay data of the second region R2 may include replacingthe overlays OV of the second region R2 measured with an orthogonalcoordinate system with the radial overlays OVR.

Then, referring to FIGS. 2, 5, and 9 , in P38, a second augmentedoverlay may be provided to the second region R2. For example, secondaugmented overlays that are overlays in a radial direction from thewafer center WC of the wafer W may be providing to the second region R2.The locations of second augmented overlays are indicated as triangularpoints in FIG. 9 . The first and second augmented overlays and themeasured overlays may be both aligned in the X direction and the Ydirection to form the rows and the columns of the grid GR.

The overlays augmented to the second region R2 may be generated byspline interpolation. The overlays augmented to the second region R2 maybe generated by fitting the measured overlays of the second region R2processed in P37 to radial positions from a center WC of the wafer W.The spline interpolation is a method of dividing the entire section bysub-sections to obtain a smooth function with a low-order polynomial.The spline interpolation provides an excellent approximation to thebehavior of a function that changes rapidly and locally, and aninterpolation result is limited to low-order polynomials. Thus, thespline interpolation provides high utility for subsequent lithographycorrection.

According to embodiments, the spline interpolation may be performedbased on an angle. In more detail, the spline interpolation may beperformed on transformed overlays on the second region R2 belonging tothe range of a split angle θd of FIG. 2 . For example, when the splitangle θd is 60 degrees as shown in FIG. 2 , the wafer W may be splitinto 6 portions, and spline interpolation may be performed on each ofthe 6 portions so that the overlay data within the second region R2 maybe augmented.

However, embodiments are not limited thereto, and the wafer W may beequally split into 2 through 5 portions or 7 or more portions accordingto the size of the split angle θd, or may be split into portions havingdifferent split angles θd.

The measured overlays in the second region R2 largely depend on thelocation in the radial direction, but, in order for the overlayregression analysis to reflect this, the number of pieces of overlaydata measured on the second region R2 is too small. In general, overlaycorrection is performed for each shot, and there are many cases wherethe number of pieces of overlay data on the second area R2 included inone shot is insufficient for regression analysis (e.g., less thanthree). Accordingly, an overlay regression analysis according to therelated art does not reflect a radial tendency appearing around thewafer W.

According to embodiments, the second augmented overlays are provided byperforming spline interpolation based on all of the measured overlays ofa plurality of external shots including the second region R2 splitaccording to the split angle θd, a sufficient number of overlay data maybe provided to perform spline interpolation. Therefore the radialtendency of the measured overlays within the second region R2 may beaccurately reflected. Furthermore, by separately adding an overlay foreach portion of the wafer W divided by the division angle θd throughspline interpolation, the tendency according to the angle of the overlaymay be reflected.

Then, referring to FIGS. 5 and 9 , in P39, an overlay regressionanalysis with respect to the external shots may be performed based onthe first and second augmented overlays.

The overlay regression analysis with respect to the external shots basedon the first and second augmented overlays is substantially the same asthe overlay regression analysis described above with reference toEquations 1 and 2, and thus, overlay parameters of the external shot maybe extracted.

Because the first and second augmented overlays form the rows andcolumns of the certain grid GR together with the measured overlays asdescribed above, a regression analysis may be performed based onoverlays uniformly distributed over the entire full shot FS, and thereliability of the overlay regression analysis may be improved.

In particular, the second augmented overlays in which the radialtendency has been reflected are provided to the second region R2 havinglarge radial tendency as in P38, and at the same time, the firstaugmented overlays are provided to the first region R1 as in P36. Thismay prevent an excessive increase in the weight of an overlay within thesecond region R2 for each external shot, and thus, the reliability ofthe overlay regression analysis may be improved.

Referring back to FIG. 1 , in P40, a lithography process may beperformed on the wafers W of a second lot, based on a result of theinspection of the wafers W of the first lot. The execution of thelithography process of P40 is similar to the execution of thelithography process of P10 described above with reference to FIGS. 1through 3B, but the lithography process of P40 may be performed based onthe result of the inspection of P30.

In more detail, the lithography process with respect to the wafers W ofthe second lot may be adjusted based on the overlay regression analysiswith respect to the first lot. The lithography process with respect tothe wafers W of the second lot may be adjusted to reduce the overlayparameters calculated by the overlay regression analysis. According tosome embodiments, adjustment factors of the lithography process withrespect to the wafers W of the second lot may include, for example, alight intensity, a scan speed, a scan direction, an offset, rotation,and size adjustment.

According to embodiments, a lot-to-lot process control for controlling aprocess for a wafer W of a subsequent lot based on the inspection resultof the wafers W included in a preceding lot has been described withreference to FIGS. 1 through 9 . However, this description is equallyapplicable to a wafer-to-wafer process control. The wafer-to-waferprocess control refers to controlling a process with respect to asubsequent wafer W included in a single lot, based on an inspectionresult of a preceding wafer W included in the same lot, or controlling aprocess on a wafer W included in another lot, based on an inspectionresult of a wafer W included in another lot.

FIG. 10 is a flowchart of a method of manufacturing a semiconductordevice, according to other embodiments.

For convenience of explanation, a description of FIG. 10 that is thesame as or similar to that given above with reference to FIGS. 1 through9 will not be repeated hereinbelow, and differences between them willnow be focused on and described.

Referring to FIGS. 2 and 10 , in operation P110, a photoresist may beprovided to a wafer W. The photoresist may be provided by theaforementioned adhesion promotion and the aforementioned spin coating.

Then, in P120, an exposure process may be performed on the wafer W. Theexecution of the exposure process may include obtaining a model functionindicating a difference between a designed pattern of an arbitraryelement previously formed on the wafer W based on the alignment markAGNM of FIG. 3A and an actually-implemented pattern as described above.

In P130, a photoresist pattern may be formed on the wafer W by adeveloping process.

In P140, the wafer W may be inspected. The inspection of the wafer W issimilar to that described above with reference to FIGS. 4 through 9 ,but may be an after-development inspection, which is an inspection afterthe developing process and before an etch process. Accordingly, anoverlay obtained in P140 may indicate a misalignment between a circuitpattern previously formed on the wafer W and the photoresist pattern.

Then, in P150, an exposure process may be evaluated. The evaluation ofthe exposure process may include comparing an overlay value with anallowable critical value. When a result of the evaluation of theexposure process is within a critical range (G), a subsequent processmay be performed, in P160. The subsequent process may include etching,ion injection, deposition, and the like. On the other hand, when theresult of the evaluation of the exposure process is not within thecritical range (NG), the photoresist pattern may be removed in P145, andthe method may proceed to P110 to provide a photoresist material layeragain.

According to some embodiments, after the method proceeds to P110 toprovide a photoresist material layer again and the exposure process isperformed in P120, a photoresist pattern may be formed, in P130. Thealignment and exposure process in P120 may depend on a result ofinspecting the wafer W in P140. In other words, the alignment andexposure process in P120 may be an alignment and exposure processcompensated by an overlay model for the same wafer W. Accordingly, theoverlay of lithography that is performed again is improved, and thus,the reliability and manufacturing yield of the manufacture of asemiconductor device may be improved.

Further processes may be performed on the wafer W, for example to form asemiconductor device. For example, additional conductive and insulatinglayers may be deposited on the wafer W to form semiconductor chips, thesemiconductor chips may then be singulated, packaged on a packagesubstrate, and encapsulated by an encapsulant to form a semiconductorpackage.

According to embodiments, re-execution of the lithography process on thewafer W based on the after-development inspection has been described.However, this description is equally applicable to the lot-to-lotprocess control described with reference to FIGS. 1 through 9 and thewafer-to-wafer process control.

FIG. 11 is a flowchart of a method of manufacturing a semiconductordevice, according to other embodiments.

For convenience of explanation, a description of FIG. 11 that is thesame as or similar to that given above with reference to FIG. 10 willnot be repeated hereinbelow, and differences between them will now befocused on and described.

Referring to FIGS. 11 , P210 and P220 may be substantially the same asP110 and P120 described above with reference to FIG. 10 , respectively.

According to some embodiments, in P230, a wafer may be inspected.According to some embodiments, the inspection of the wafer may includeobtaining an overlay of a photoresist material layer after exposurebefore development. In this case, a refractive index difference betweenexposed portions of the photoresist material layer and non-exposedportions thereof may be very small. Thus, a latent image of thephotoresist material layer before development has very low contrast.According to some embodiments, before the inspection is performed,contrast between the exposed portions and non-exposed portions of thephotoresist material layer may be increased by an after-exposure bakeprocess.

The inspection of the wafer in P230 may be similar to the inspection ofthe wafer in P30. As the inspection of the wafer in P230 is performed,an overlay between a latent image formed on the photoresist materiallayer and a semiconductor layer where a circuit pattern has been alreadyformed may be measured, and an overlay model indicating an overlay of anarbitrary element on the wafer W may be obtained based on the value ofthe measured overlay.

Then, in P240, a lithography process may be evaluated. The evaluation ofthe lithography process may include comparing the overlay with anallowable critical value (G).

When the overlay is less than or equal to the allowable critical value(G), a photoresist pattern may be formed through development in P250,and a subsequent process such as etching, ion injection, and/ordeposition may be performed in P260.

On the other hand, when the overlay exceeds the allowable critical value(NG), the photoresist material layer may be removed in P245, and,similar to FIG. 10 , P210 through P230 may be performed again. In thiscase, the exposure process in P220 may be performed to correct theoverlay model calculated in P230.

Further processes may be performed on the wafer W, for example to form asemiconductor device. For example, additional conductive and insulatinglayers may be deposited on the wafer W to form semiconductor chips, thesemiconductor chips may then be singulated, packaged on a packagesubstrate, and encapsulated by an encapsulant to form a semiconductorpackage.

According to embodiments, re-execution of the lithography process on thewafer W based on an inspection after exposure before development hasbeen described. However, this description is equally applicable to thelot-to-lot process control described with reference to FIGS. 1 through 9and the wafer-to-wafer process control.

While the inventive concept has been particularly shown and describedwith reference to embodiments thereof, it will be understood thatvarious changes in form and details may be made therein withoutdeparting from the spirit and scope of the following claims.

What is claimed is:
 1. A method of manufacturing a semiconductor device,the method comprising: transferring an internal shot and an externalshot by performing a lithography process and a patterning process basedon the lithography process on a first wafer, wherein the internal shotis within a critical radius from a center of the first wafer, and theexternal shot includes a first region within the critical radius fromthe center of the first wafer and a second region outside the criticalradius; measuring an overlay of the first wafer patterned by thepatterning process; analyzing the overlay of the first wafer; andperforming a lithography process on a second wafer, based on theanalyzing of the overlay of the first wafer, wherein the analyzing ofthe overlay of the first wafer comprises: providing, to the firstregion, first augmented overlays generated based on an orthogonalcoordinate system using first and second directions perpendicular toeach other as an axis; and providing, to the second region, secondaugmented overlays that are overlays in a radial direction from thecenter of the first wafer.
 2. The method of claim 1, wherein locationsof the first augmented overlays and locations of the second augmentedoverlays are aligned in the first and second directions to constitute agrid.
 3. The method of claim 1, further comprising: before the providingof the second augmented overlays, processing overlays of the secondregion such that the overlays are parallel to the radial direction. 4.The method of claim 1, wherein a plurality of external shots aretransferred to the first wafer, and wherein the second augmentedoverlays are provided by interpolation based on the measured overlays ofthe plurality of external shots.
 5. The method of claim 4, wherein thefirst augmented overlays of each of the external shot are provided basedon the measured overlays of corresponding one of the plurality ofexternal shots.
 6. The method of claim 1, wherein the second augmentedoverlays are generated by spline interpolation.
 7. The method of claim1, wherein the second augmented overlays are generated by interpolationusing a radial distance from the center of the first wafer as a singleparameter.
 8. The method of claim 1, further comprising: calculating anoverlay model function over an entire surface of the external shot,based on the first and second augmented overlays.
 9. A method ofmanufacturing a semiconductor device, the method comprising:transferring a circuit pattern on an extreme ultraviolet (EUV) photomaskto a photoresist layer formed on a wafer, wherein a plurality of shotsthat are portions of the wafer to which the circuit pattern on the EUVphotomask has been transferred include a first region within a criticalradius from a center of the wafer and a second region outside thecritical radius; forming a photoresist pattern having a shapecorresponding to the EUV photomask, by developing the photoresist; andinspecting the photoresist pattern, wherein the inspecting of thephotoresist pattern comprises: measuring overlays indicatingmisalignment between a pattern formed below a photoresist of the secondregion and the photoresist pattern; processing the overlays of thesecond region such that the overlays of the second region are parallelto a radial direction; and providing, to a plurality of locations on thesecond region, first augmented overlays in the radial direction from thecenter of the wafer, based on the processed overlays.
 10. The method ofclaim 9, wherein the first augmented overlays of the second regionextend in the radial direction.
 11. The method of claim 9, wherein thefirst augmented overlays of the second region are based on the overlaysin the second regions of the plurality of shots.
 12. The method of claim9, wherein the first augmented overlays of the second region aregenerated by interpolation using a radial distance from the center ofthe wafer as a single parameter.
 13. The method of claim 9, furthercomprising: adding second augmented overlays to a plurality of locationson the first region, based on overlays of the first region.
 14. Themethod of claim 13, wherein the second augmented overlays of the firstregion and the first augmented overlays of the second region are alignedin rows and columns to form a grid.
 15. The method of claim 13, furthercomprising: calculating an overlay model representing an overlay for anarbitrary location of the shot, based on the first and second augmentedoverlays.
 16. The method of claim 9, wherein, when the photoresistpattern is defective as a result of inspecting the photoresist pattern,the photoresist pattern is removed.
 17. The method of claim 16, furthercomprising: providing a photoresist onto the wafer again and exposingthe wafer, based on a result of inspecting the wafer.
 18. A method ofmanufacturing a semiconductor device, the method comprising:transferring a circuit pattern on a photomask to a wafer, wherein eachof a plurality of shots that are portions of the wafer to which thecircuit pattern on the photomask has been transferred includes a firstregion within a critical radius from a center of the wafer and a secondregion outside the critical radius; measuring overlays representing aninterlayered misalignment of the plurality of shots; providing firstaugmented overlays to the first region of a first shot from among theplurality of shots, based on overlays included in the first region ofthe first shot; providing second augmented overlays to the second regionof the first shot, based on overlays included in the plurality of shots;and calculating an overlay model representing an overlay of an arbitrarylocation on the entire surface of the first shot by regression analysisof the first and second augmented overlays.
 19. The method of claim 18,wherein at least some of the first augmented overlays extend in adirection intersecting with a radial direction with respect to thecenter of the wafer.
 20. The method of claim 18, wherein the secondaugmented overlays extend in a radial direction with respect to thecenter of the wafer.